
For efficient inference schemes, auxiliary variables \(m_1, \dots , m_K\)  can be introduced [1]}, [2]}:
\(& p(n,m \mid \alpha ) =\frac{\Gamma (\sum _{k=1}^K \alpha _{k})}{\Gamma (\sum _{k=1}^K \alpha _{k} + n_{k})}\prod _{k=1}^K\operatorname{s}(m_{k},n_{k}) \cdot \left( \alpha _{k}\right)^{m_k}\) 
